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    the function checks that each element of the array_like object is equal to
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    That is, AssertionError is not raised if both objects have NaNs in the same
    positions.  This is in contrast to the IEEE standard on NaNs, which says
    that NaN compared to anything must return False.

    Parameters
    ----------
    actual : array_like
        The object to check.
    desired : array_like
        The expected object.
    err_msg : str, optional
        The error message to be printed in case of failure.
    verbose : bool, optional
        If True, the conflicting values are appended to the error message.

    Raises
    ------
    AssertionError
        If actual and desired are not equal.

    Examples
    --------
    >>> np.testing.assert_equal([4,5], [4,6])
    Traceback (most recent call last):
        ...
    AssertionError:
    Items are not equal:
    item=1
     ACTUAL: 5
     DESIRED: 6

    The following comparison does not raise an exception.  There are NaNs
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    test_string : str
        The message supplied to AssertionError.
    actual : object
        The object to test for equality against `desired`.
    desired : object
        The expected result.

    Examples
    --------
    >>> np.testing.print_assert_equal('Test XYZ of func xyz', [0, 1], [0, 1])
    >>> np.testing.print_assert_equal('Test XYZ of func xyz', [0, 1], [0, 2])
    Traceback (most recent call last):
    ...
    AssertionError: Test XYZ of func xyz failed
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              `assert_array_almost_equal_nulp` or `assert_array_max_ulp`
              instead of this function for more consistent floating point
              comparisons.

    The test verifies that the elements of ``actual`` and ``desired`` satisfy.

        ``abs(desired-actual) < 1.5 * 10**(-decimal)``

    That is a looser test than originally documented, but agrees with what the
    actual implementation in `assert_array_almost_equal` did up to rounding
    vagaries. An exception is raised at conflicting values. For ndarrays this
    delegates to assert_array_almost_equal

    Parameters
    ----------
    actual : array_like
        The object to check.
    desired : array_like
        The expected object.
    decimal : int, optional
        Desired precision, default is 7.
    err_msg : str, optional
        The error message to be printed in case of failure.
    verbose : bool, optional
        If True, the conflicting values are appended to the error message.

    Raises
    ------
    AssertionError
      If actual and desired are not equal up to specified precision.

    See Also
    --------
    assert_allclose: Compare two array_like objects for equality with desired
                     relative and/or absolute precision.
    assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

    Examples
    --------
    >>> import numpy.testing as npt
    >>> npt.assert_almost_equal(2.3333333333333, 2.33333334)
    >>> npt.assert_almost_equal(2.3333333333333, 2.33333334, decimal=10)
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not almost equal to 10 decimals
     ACTUAL: 2.3333333333333
     DESIRED: 2.33333334

    >>> npt.assert_almost_equal(np.array([1.0,2.3333333333333]),
    ...                         np.array([1.0,2.33333334]), decimal=9)
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not almost equal to 9 decimals
    <BLANKLINE>
    Mismatched elements: 1 / 2 (50%)
    Max absolute difference: 6.66669964e-09
    Max relative difference: 2.85715698e-09
     x: array([1.         , 2.333333333])
     y: array([1.        , 2.33333334])

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    Raises an AssertionError if two items are not equal up to significant
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              `assert_array_almost_equal_nulp` or `assert_array_max_ulp`
              instead of this function for more consistent floating point
              comparisons.

    Given two numbers, check that they are approximately equal.
    Approximately equal is defined as the number of significant digits
    that agree.

    Parameters
    ----------
    actual : scalar
        The object to check.
    desired : scalar
        The expected object.
    significant : int, optional
        Desired precision, default is 7.
    err_msg : str, optional
        The error message to be printed in case of failure.
    verbose : bool, optional
        If True, the conflicting values are appended to the error message.

    Raises
    ------
    AssertionError
      If actual and desired are not equal up to specified precision.

    See Also
    --------
    assert_allclose: Compare two array_like objects for equality with desired
                     relative and/or absolute precision.
    assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

    Examples
    --------
    >>> np.testing.assert_approx_equal(0.12345677777777e-20, 0.1234567e-20)
    >>> np.testing.assert_approx_equal(0.12345670e-20, 0.12345671e-20,
    ...                                significant=8)
    >>> np.testing.assert_approx_equal(0.12345670e-20, 0.12345672e-20,
    ...                                significant=8)
    Traceback (most recent call last):
        ...
    AssertionError:
    Items are not equal to 8 significant digits:
     ACTUAL: 1.234567e-21
     DESIRED: 1.2345672e-21

    the evaluated condition that raises the exception is

    >>> abs(0.12345670e-20/1e-21 - 0.12345672e-20/1e-21) >= 10**-(8-1)
    True

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cCsd}ttj||||dd�dS)al

    Raises an AssertionError if two array_like objects are not equal.

    Given two array_like objects, check that the shape is equal and all
    elements of these objects are equal (but see the Notes for the special
    handling of a scalar). An exception is raised at shape mismatch or
    conflicting values. In contrast to the standard usage in numpy, NaNs
    are compared like numbers, no assertion is raised if both objects have
    NaNs in the same positions.

    The usual caution for verifying equality with floating point numbers is
    advised.

    Parameters
    ----------
    x : array_like
        The actual object to check.
    y : array_like
        The desired, expected object.
    err_msg : str, optional
        The error message to be printed in case of failure.
    verbose : bool, optional
        If True, the conflicting values are appended to the error message.

    Raises
    ------
    AssertionError
        If actual and desired objects are not equal.

    See Also
    --------
    assert_allclose: Compare two array_like objects for equality with desired
                     relative and/or absolute precision.
    assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

    Notes
    -----
    When one of `x` and `y` is a scalar and the other is array_like, the
    function checks that each element of the array_like object is equal to
    the scalar.

    Examples
    --------
    The first assert does not raise an exception:

    >>> np.testing.assert_array_equal([1.0,2.33333,np.nan],
    ...                               [np.exp(0),2.33333, np.nan])

    Assert fails with numerical imprecision with floats:

    >>> np.testing.assert_array_equal([1.0,np.pi,np.nan],
    ...                               [1, np.sqrt(np.pi)**2, np.nan])
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not equal
    <BLANKLINE>
    Mismatched elements: 1 / 3 (33.3%)
    Max absolute difference: 4.4408921e-16
    Max relative difference: 1.41357986e-16
     x: array([1.      , 3.141593,      nan])
     y: array([1.      , 3.141593,      nan])

    Use `assert_allclose` or one of the nulp (number of floating point values)
    functions for these cases instead:

    >>> np.testing.assert_allclose([1.0,np.pi,np.nan],
    ...                            [1, np.sqrt(np.pi)**2, np.nan],
    ...                            rtol=1e-10, atol=0)

    As mentioned in the Notes section, `assert_array_equal` has special
    handling for scalars. Here the test checks that each value in `x` is 3:

    >>> x = np.full((2, 5), fill_value=3)
    >>> np.testing.assert_array_equal(x, 3)

    TzArrays are not equal)r�r!r�N)r2�operator�__eq__)rOr�r�r!rIr<r<r=rSsNc	sjd}ddlm�m�m�m�ddlm�ddlm��������fdd�}t	|||||d��d	�d
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    Raises an AssertionError if two objects are not equal up to desired
    precision.

    .. note:: It is recommended to use one of `assert_allclose`,
              `assert_array_almost_equal_nulp` or `assert_array_max_ulp`
              instead of this function for more consistent floating point
              comparisons.

    The test verifies identical shapes and that the elements of ``actual`` and
    ``desired`` satisfy.

        ``abs(desired-actual) < 1.5 * 10**(-decimal)``

    That is a looser test than originally documented, but agrees with what the
    actual implementation did up to rounding vagaries. An exception is raised
    at shape mismatch or conflicting values. In contrast to the standard usage
    in numpy, NaNs are compared like numbers, no assertion is raised if both
    objects have NaNs in the same positions.

    Parameters
    ----------
    x : array_like
        The actual object to check.
    y : array_like
        The desired, expected object.
    decimal : int, optional
        Desired precision, default is 6.
    err_msg : str, optional
      The error message to be printed in case of failure.
    verbose : bool, optional
        If True, the conflicting values are appended to the error message.

    Raises
    ------
    AssertionError
        If actual and desired are not equal up to specified precision.

    See Also
    --------
    assert_allclose: Compare two array_like objects for equality with desired
                     relative and/or absolute precision.
    assert_array_almost_equal_nulp, assert_array_max_ulp, assert_equal

    Examples
    --------
    the first assert does not raise an exception

    >>> np.testing.assert_array_almost_equal([1.0,2.333,np.nan],
    ...                                      [1.0,2.333,np.nan])

    >>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],
    ...                                      [1.0,2.33339,np.nan], decimal=5)
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not almost equal to 5 decimals
    <BLANKLINE>
    Mismatched elements: 1 / 3 (33.3%)
    Max absolute difference: 6.e-05
    Max relative difference: 2.57136612e-05
     x: array([1.     , 2.33333,     nan])
     y: array([1.     , 2.33339,     nan])

    >>> np.testing.assert_array_almost_equal([1.0,2.33333,np.nan],
    ...                                      [1.0,2.33333, 5], decimal=5)
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not almost equal to 5 decimals
    <BLANKLINE>
    x and y nan location mismatch:
     x: array([1.     , 2.33333,     nan])
     y: array([1.     , 2.33333, 5.     ])

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    second object. An exception is raised at shape mismatch or incorrectly
    ordered values. Shape mismatch does not raise if an object has zero
    dimension. In contrast to the standard usage in numpy, NaNs are
    compared, no assertion is raised if both objects have NaNs in the same
    positions.



    Parameters
    ----------
    x : array_like
      The smaller object to check.
    y : array_like
      The larger object to compare.
    err_msg : string
      The error message to be printed in case of failure.
    verbose : bool
        If True, the conflicting values are appended to the error message.

    Raises
    ------
    AssertionError
      If actual and desired objects are not equal.

    See Also
    --------
    assert_array_equal: tests objects for equality
    assert_array_almost_equal: test objects for equality up to precision



    Examples
    --------
    >>> np.testing.assert_array_less([1.0, 1.0, np.nan], [1.1, 2.0, np.nan])
    >>> np.testing.assert_array_less([1.0, 1.0, np.nan], [1, 2.0, np.nan])
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not less-ordered
    <BLANKLINE>
    Mismatched elements: 1 / 3 (33.3%)
    Max absolute difference: 1.
    Max relative difference: 0.5
     x: array([ 1.,  1., nan])
     y: array([ 1.,  2., nan])

    >>> np.testing.assert_array_less([1.0, 4.0], 3)
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not less-ordered
    <BLANKLINE>
    Mismatched elements: 1 / 2 (50%)
    Max absolute difference: 2.
    Max relative difference: 0.66666667
     x: array([1., 4.])
     y: array(3)

    >>> np.testing.assert_array_less([1.0, 2.0, 3.0], [4])
    Traceback (most recent call last):
        ...
    AssertionError:
    Arrays are not less-ordered
    <BLANKLINE>
    (shapes (3,), (1,) mismatch)
     x: array([1., 2., 3.])
     y: array([4])

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    actual : str
        The string to test for equality against the expected string.
    desired : str
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    Examples
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    >>> np.testing.assert_string_equal('abc', 'abc')
    >>> np.testing.assert_string_equal('abc', 'abcd')
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    Notes
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    .. warning::
       This decorator is nose specific, do not use it if you are using a
       different test framework.

    Parameters
    ----------
    args : exceptions
        The test passes if any of the passed exceptions is raised.

    Raises
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    AssertionError

    Examples
    --------

    Usage::

        @raises(TypeError, ValueError)
        def test_raises_type_error():
            raise TypeError("This test passes")

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    thrown, it will not be caught, and the test case will be
    deemed to have suffered an error, exactly as for an
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    Parameters
    ----------
    cls : class
        Class whose methods to decorate.
    decorator : function
        Decorator to apply to methods
    testmatch : compiled regexp or str, optional
        The regular expression. Default value is None, in which case the
        nose default (``re.compile(r'(?:^|[\b_\.%s-])[Tt]est' % os.sep)``)
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    timing accuracy.

    Parameters
    ----------
    code_str : str
        The code to be timed.
    times : int, optional
        The number of times the code is executed. Default is 1. The code is
        only compiled once.
    label : str, optional
        A label to identify `code_str` with. This is passed into ``compile``
        as the second argument (for run-time error messages).

    Returns
    -------
    elapsed : float
        Total elapsed time in seconds for executing `code_str` `times` times.

    Examples
    --------
    >>> times = 10
    >>> etime = np.testing.measure('for i in range(1000): np.sqrt(i**2)', times=times)
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    between `actual` and `desired` to ``atol + rtol * abs(desired)``.

    .. versionadded:: 1.5.0

    Parameters
    ----------
    actual : array_like
        Array obtained.
    desired : array_like
        Array desired.
    rtol : float, optional
        Relative tolerance.
    atol : float, optional
        Absolute tolerance.
    equal_nan : bool, optional.
        If True, NaNs will compare equal.
    err_msg : str, optional
        The error message to be printed in case of failure.
    verbose : bool, optional
        If True, the conflicting values are appended to the error message.

    Raises
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    AssertionError
        If actual and desired are not equal up to specified precision.

    See Also
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    assert_array_almost_equal_nulp, assert_array_max_ulp

    Examples
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    >>> x = [1e-5, 1e-3, 1e-1]
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        The maximum number of unit in the last place for tolerance (see Notes).
        Default is 1.

    Returns
    -------
    None

    Raises
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    AssertionError
        If the spacing between `x` and `y` for one or more elements is larger
        than `nulp`.

    See Also
    --------
    assert_array_max_ulp : Check that all items of arrays differ in at most
        N Units in the Last Place.
    spacing : Return the distance between x and the nearest adjacent number.

    Notes
    -----
    An assertion is raised if the following condition is not met::

        abs(x - y) <= nulps * spacing(maximum(abs(x), abs(y)))

    Examples
    --------
    >>> x = np.array([1., 1e-10, 1e-20])
    >>> eps = np.finfo(x.dtype).eps
    >>> np.testing.assert_array_almost_equal_nulp(x, x*eps/2 + x)

    >>> np.testing.assert_array_almost_equal_nulp(x, x*eps + x)
    Traceback (most recent call last):
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    AssertionError: X and Y are not equal to 1 ULP (max is 2)

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        `b` can differ. Default is 1.
    dtype : dtype, optional
        Data-type to convert `a` and `b` to if given. Default is None.

    Returns
    -------
    ret : ndarray
        Array containing number of representable floating point numbers between
        items in `a` and `b`.

    Raises
    ------
    AssertionError
        If one or more elements differ by more than `maxulp`.

    Notes
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    For computing the ULP difference, this API does not differentiate between
    various representations of NAN (ULP difference between 0x7fc00000 and 0xffc00000
    is zero).

    See Also
    --------
    assert_array_almost_equal_nulp : Compare two arrays relatively to their
        spacing.

    Examples
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        Data-type to convert `x` and `y` to if given. Default is None.

    Returns
    -------
    nulp : array_like
        number of representable floating point numbers between each item in x
        and y.

    Notes
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    For computing the ULP difference, this API does not differentiate between
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    Examples
    --------
    # By definition, epsilon is the smallest number such as 1 + eps != 1, so
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